On Ball Numbers

We first shortly review, in part throwing a new light on, basics of ball numbers for balls having a positively homogeneous Minkowski functional and turn over then to a new particular class of ball numbers of balls having a Minkowski functional being homogeneous with respect to multiplication with a...

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Main Author:	Wolf-Dieter Richter
Format:	Article
Language:	English
Published:	MDPI AG 2019-08-01
Series:	Mathematics
Subjects:	norm and antinorm ball matrix homogeneous ball star body star radius norm and antinorm radius <i>p</i>-spherical radius parameter dual surface content measure density normalizing constant crystal breeding temperature expansion
Online Access:	https://www.mdpi.com/2227-7390/7/8/738

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spelling	doaj-4d5dee0cc9f14333965a4b0258ae94652020-11-25T01:34:01ZengMDPI AGMathematics2227-73902019-08-017873810.3390/math7080738math7080738On Ball NumbersWolf-Dieter Richter0Institute of Mathematics, University of Rostock, Ulmenstraße 69, Haus 3, 18057 Rostock, GermanyWe first shortly review, in part throwing a new light on, basics of ball numbers for balls having a positively homogeneous Minkowski functional and turn over then to a new particular class of ball numbers of balls having a Minkowski functional being homogeneous with respect to multiplication with a specific diagonal matrix. Applications to crystal breeding, temperature expansion and normalizing density generating functions in big data analysis are indicated and a challenging problem from the inhomogeneity program is stated.https://www.mdpi.com/2227-7390/7/8/738norm and antinorm ballmatrix homogeneous ballstar bodystar radiusnorm and antinorm radius<i>p</i>-spherical radius parameterdual surface content measuredensity normalizing constantcrystal breedingtemperature expansion
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Wolf-Dieter Richter
spellingShingle	Wolf-Dieter Richter On Ball Numbers Mathematics norm and antinorm ball matrix homogeneous ball star body star radius norm and antinorm radius <i>p</i>-spherical radius parameter dual surface content measure density normalizing constant crystal breeding temperature expansion
author_facet	Wolf-Dieter Richter
author_sort	Wolf-Dieter Richter
title	On Ball Numbers
title_short	On Ball Numbers
title_full	On Ball Numbers
title_fullStr	On Ball Numbers
title_full_unstemmed	On Ball Numbers
title_sort	on ball numbers
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2019-08-01
description	We first shortly review, in part throwing a new light on, basics of ball numbers for balls having a positively homogeneous Minkowski functional and turn over then to a new particular class of ball numbers of balls having a Minkowski functional being homogeneous with respect to multiplication with a specific diagonal matrix. Applications to crystal breeding, temperature expansion and normalizing density generating functions in big data analysis are indicated and a challenging problem from the inhomogeneity program is stated.
topic	norm and antinorm ball matrix homogeneous ball star body star radius norm and antinorm radius <i>p</i>-spherical radius parameter dual surface content measure density normalizing constant crystal breeding temperature expansion
url	https://www.mdpi.com/2227-7390/7/8/738
work_keys_str_mv	AT wolfdieterrichter onballnumbers
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On Ball Numbers

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